Statistics Nonlinear Cox Proportional Hazards Model Analysis

In medicine, the assessment and prediction of survival time is an important research task, and survival time is can be defined as from a starting event reaches a certain point events experienced by the time span. In epidemiological studies, from the beginning of exposure to risk factors to the onset time etc. as survival time. Survival time research involves many fields in basic science and technical science in which statistical methods play an important role. From the mathematical point of view, survival analysis is a type of statistical analysis towards one or more non-negative random variables (survival time) in the field of bio-medical and engineering technology, which is becoming an important branch of modern mathematics statistics.In medicine, there are3general approaches to analysis survival data:non-parametric analysis, semi-parametric models and parametric models. Non-parametric analysis are limited to evaluating the effect of one, or a small number of, qualitative variables on survival times, However, we often want to simultaneously evaluate the effects of multiple continuous or categorical explanatory variables. Multivariable technique is needed in our paper. The most commonly used form of multivariable analysis for survival data is the proportional hazards model (also known as the Cox regression model)(Cox,1972). It is a semi-parametric model in that we do not have to assume any specific functional form for the hazard, but we do model the ratio of hazards as a linear function of the predictors.As the method of multivariable survival analysis, Cox models have a very wide application., but there are no relevant results in the nonlinear Cox model studies. This paper mainly discusses the relevant results in the nonlinear Cox model studies with right-censored data. The first chapter of this paper mainly analyzes the background of the nonlinear Cox proportional hazards model, model of the basic concept and the main research work. The second chapter mainly studies nonlinear Cox proportional hazard models, the likelihood function and fitting, and the model is applied to do more detailed analysis. The third chapter discusses the confidence region of nonlinear Cox models. The fourth chapter covers the evaluation of model, including evaluating the proportional hazards assumption, evaluating the overall fit of the model and the detection of the abnormal points.Through the study of this article can increase people to the deep understanding of the nonlinear Cox regression model, and this study can further enhance the theory and application of the model.